一种计算交通波传播速度的方法

基于交通心理学和车辆跟驰的物理机制推导出一种交通波传播速度公式, 可以用于计算各种车流状态下的波速. 应用交通波传播速度公式计算了平面交叉口红灯变为绿灯时的起动波波速, 通过与实测数据比较, 证实了该计算方法的可行性.在此基础上推导了交通波速的特性, 以事故波波速特性为例进行了详细讨论, 所得结果符合交通实际.      

一个新的空间掩盖效应拟合公式

传统的空间掩盖效应是采用韦伯（Weber）定律来描述的，然而该定律仅考虑了明视觉区，对较弱或较强的光强均不合适。为了更好地描述空间掩盖效应，本文利用信号处理方法，给出了一种新的拟合公式。实验用不同模型拟合Konig与Brodhun的实验数据，证实了提出的模型均方根误差仅为0．0102，小于传统的Weber定律、Weber定律的优选表达式、Guilford模型，以及Chen模型。结果表明，提出的拟合公式在更宽的光强范围内都能与数据很好地拟合，可更广泛地用于工程实践。     

Carl Neumann’s Contributions to Electrodynamics

I examine the publications of Carl Neumann (1832–1925) on electrodynamics, which constitute a major part of his work and which illuminate his approach to mathematical physics. I show how Neumann contributed to physics at an important stage in its development and how his work led to a polemic with Hermann Helmholtz (1821–1894). Neumann advanced and extended the ideas of the Königsberg school of mathematical physics. His investigations were aimed at founding a mathematically exact physical theory of electrodynamics, following the approach of Carl G.J. Jacobi (1804–1851) on the foundation of a physical theory as outlined in Jacobis lectures on analytical mechanics. Neumanns work also shows how he clung to principles that impeded him in appreciating and developing new ideas such as those on field theory that were proposed by Michael Faraday (1791–1867) and James Clerk Maxwell (1831–1879).Karl-Heinz Schlote works as a historian of mathematics in the Arbeitsgruppe für Geschichte der Naturwissenschaften und Mathematik at the Sächsische Akademie der Wissenschaften in Leipzig, Germany.     

Uniform asymptotic formulae for the spheroidal angular function

The problem of wave scattering by a spheroid is treated. Special interest is paid to the solution of the differential wave equation related to the angular spheroidal functions. A solution is obtained using uniform asymptotic formulae along with semiclassical methods. The developed method shows that it is possible to interpolate uniformly the spheroidal angular function with Weber's parabolic cylindric functions and Legendre's functions.     

On the Fermat–Weber center of a convex object

We show that for any convex object Q in the plane, the average distance from the Fermat–Weber center of Q to the points in Q is at least Δ(Q)/7, where Δ(Q) is the diameter of Q, and that there exists a convex object P for which this distance is Δ(P)/6. We use this result to obtain a linear-time approximation scheme for finding an approximate Fermat–Weber center of a convex polygon Q.     

On the use of the Varignon frame for single facility Weber problems in the presence of convex barriers

This paper presents a new experimental approach to the Weber problem in the presence of convex barriers by using the Varignon frame. The Varignon frame is a mechanical system of strings, weights and a board with holes that has been used to identify an optimal location for the classical Weber problem. We show through analytical results that the same analog can also be used for some of the Weber problems in the presence of barriers. Some examples from the literature are revisited through experiments. Findings are compared to those found in the literature. Practical use of the analog is discussed as it provides rapid solutions, allows for flexibility, and enables one to visualize the problem.     

Planar weber location problems with line barriers

The Weber problem for a given finite set of existing facilities in the plane is to find the location of a new facility such that the weithted sum of distances to the existing facilities is minimized.

A variation of this problem is obtained if the existing facilities are situated on two sides of a linear barrier. Such barriers like rivers, highways, borders or mountain ranges are frequently encountered in practice.

Structural results as well as algorithms for this non-convex optimization problem depending on the distance function and on the number and location of passages through the barrier are presented.     

An Order-theoretic Framework for the Greedy Algorithm with Applications to the Core and Weber Set of Cooperative Games

An algebraic model generalizing submodular polytopes is presented, where modular functions on partially ordered sets take over the role of vectors in R ⁿ . This model unifies various generalizations of combinatorial models in which the greedy algorithm and the Monge algorithm are successful and generalizations of the notions of core and Weber set in cooperative game theory.As a further application, we show that an earlier model of ours as well as the algorithmic model of Queyranne, Spieksma and Tardella for the Monge algorithm can be treated within the framework of usual matroid theory (on unordered ground-sets), which permits also the efficient algorithmic solution of the intersection problem within this model.